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24 July, 22:03

The manager of a radio station decides that on each successive evening (7 days per week), a Beethoven piano sonata will be played followed by a Beethoven symphony followed by a Beethoven piano concerto. For how many years could this policy be continued before exactly the same program would have to be repeated? (Assume there are 365 days in a year. Round your answer up to the nearest whole number.)

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  1. 24 July, 22:19
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    3 years, 11 months and 10 days

    Step-by-step explanation:

    Beethoven wrote

    32 piano sonatas

    9 symphonies

    5 piano concertos

    By the fundamental principle of counting there are

    32 times 9 times 5 ways of combining these pieces in the required order.

    32 times 9 times 5 = 1,440

    As there are 365 days in a year, the policy decided by the manager could be continued during

    1,440/365 = 3.9452 years.

    But 3.9452 years = 3 years + 0.9452 years.

    As 1 year equals 12 months

    0.9452 years = 11.3424 months

    11.3424 months = 11 months+0.3424 months

    As 1 month = 30 days

    0.3424 months = 10.27 days = 10 days rounded to the nearest integer

    So, the manager could continue this policy for

    3 years, 11 months and 10 days without repeating the program.
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